1. Field of the Invention
This invention relates to a power system stabilizing apparatus with a power system stabilizer (PSS) for a synchronous generator.
2. Description of the Prior Art
Automatic voltage regulators (AVR) have been widely applied with the output thereof being transmitted to the exciter for controlling the field current in order to maintain the terminal voltage of the synchronous generator at a constant predetermined level. However, if the response of the AVR is too quick, a negative control effect may take place in the synchronous generator, resulting in a disorder of the overall system stabilization. Therefore, the power system stabilizing apparatus with PSS is applied to prevent such a disorder effect.
FIG. 1 shows a block diagram of the power system stabilizing apparatus for a synchronous generator, which is disclosed in Japanese Patent Publication No. 53-44204 (1978).
Referring to FIg. 1, 1 designates an input terminal giving a deviation from the reference terminal voltage of a generator, 2 designates PSS, 3 designates the input terminal of the PSS 2, 4 designates a damping circuit, 5 designates an adder circuit subtracting the output of the damping circuit 4 from the sum of the deviation from the input terminal 1 and the output of the PSS 2, 6 designates an AVR controlling an exciter 7 by the output of the above adder circuit 4 and 7 designates an exciter, which is controlled by the above AVR 6, so as to supply the field current to the generator (not shown), while 2a designates a filter circuit which is used to define the domain range of the PSS 2 corresponding to input signals 3 of the PSS 2 and featured with the transfer function; ##EQU1## where T.sub.R and T.sub.H are the time constants of the set filter constructing the above filter circuit 2a and of the high pass filter respectively.
On the other hand, 2b is a phase compensation circuit for time delays of the AVR 6, the exciter 7, the generator, etc. and is an advance/delay circuit with an amplification effect, which is normally represented in the form; ##EQU2## where K is a gain of the PSS 2 while T.sub.11 and T.sub.12 are a delay time constant and an advance time constant respectively.
Furthermore, 2c designates a limiter which limits the output signals of the PSS 2 to a signal level appropriate for the entire exciting system shown in FIG. 4. Usually, revolution deviation of the generator rotor, frequency deviation of the generator terminal voltage, output deviation of the generator itself, etc. are used as the input signals of the PSS 2.
Now the power system stabilizing apparatus actions will be described. When the terminal voltage of the generator deviates from its reference value, the input terminal receives the corresponding deviation signal, which is amplified by the AVR 6 and input to the exciter 7, where the deviation signal is further amplified, supplied to the field windings of the generator and so controlled such that the deviation of the generator terminal voltage from its reference value returns to zero. The damping circuit 4 is used to stabilize the above control action and to feedback the output therefrom to the adder circuit 5, as mentioned before. The output of the PSS 2 is added supplementarily to such a control in order to improve the stabilization of the power system.
Supposing that the input signal to the PSS 2 is a revolution deviation, the filter circuit 2a cuts off the direct current and high frequency portion of this input signal, which is then input to the amplification and phase compensation circuit 2b for amplification and phase compensation. The amplification and phase compensation circuit 2b is controlled to less than its appropriate level through the limiter 2c and then fed to the adder circuit 5. Therefore, the output of the exciter 7 is controlled in such a manner that drift motion of the generator can be prevented.
Now, the function of the PSS 2 will be described. FIG. 2 shows a block diagram with linear approximation of drift motion of a generator representing a one-machine infinite system as described, for instance, in Bulletin of Electric Cooperative Researches, Vol. 34, No. 5. In FIG. 2, K.sub.1 means a synchronizing torque factor to be generated by a generator with constant field crossing fluxes, K.sub.1 ' means the synchronizing torque factor to be generated by the AVR and K.sub.1 " means the synchronizing torque factor to be generated by the PSS 2, while D means a braking torque factor to be generated by the generator with constant field crossing fluxes, D' means a braking torque factor to be generated by the AVR 6 and D" means a braking torque factor to be generated by the PSS 2.
Moreover,
.DELTA.T.sub.M indicates the mechanical input torque deviation, PA1 M indicates the inertial constant of the generator, PA1 .DELTA..omega. indicates the revolution deviation, PA1 .omega..sub.O indicates the reference revolution and PA1 .DELTA..theta. indicates the phase difference angle deviation. PA1 .DELTA.T.sub.M, .DELTA..omega. and .DELTA..theta. can be expressed in the differential equation given below. The equation is in the same form of, the so-called, equation of motion of secondary system. ##EQU3## wherein EQU D*=D+D'+D" EQU K*=K+K'+K"
This equation of motion is Laplacetransformed into the transfer function, which is represented in FIG. 2. Since .DELTA.T.sub.M is a torque, that is, an angle acceleration power, .DELTA..omega. is a number of revolution, that is, an angle velocity, .DELTA..theta. is an angle, it may be well concluded that the relationship among them is; the angle velocity is gained by integrating the angle acceleration force, and the angle is gained by integrating angle velocity. Accordingly, it can be said that both the blocks of (1/MS) and (.omega..sub.O /s) in FIG. 2 represent integrators whose time constants are M and (1/.omega..sub.O) respectively.
Generally speaking, D' tends to take a negative value in cases where the phase angle .theta. increases at a power factor being near 1.0. Particularly when the AVR 6 with quick response and high gain is used, the value of D+D' becomes negative sometimes, resulting in failure of static stability due to insufficient braking power. In such cases, the PSS 2 is added to generate the braking power D" for the stabilization required.
The above stabilizing effect is illustrated in FIG. 3, where the synchronizing torque and the braking torque are taken as the abscissa and the ordinate respectively. Both the synchronizing torque and the braking torque of a synchronous generator with constant field crossing fluxes are positive, and the sum of the torques (shown as K.sub.1 +D) is found in the first quadrant, while the braking torque to be generated by the AVR 6 being negative, the sum of the braking torque and the synchronizing torque (shown as K.sub.1 '+D') is found in the forth quadrant. The sum of the torques generated by the AVR 6 and the generator with constant field crossing fluxes (shown as K.sub.1 +K.sub.1 '+D+D') takes a value of approximately equal to zero or sometimes a negative value, resulting in failure of the static stabilization. When the PSS 2 gives a braking torque (whose sum with the synchronizing torque K.sub.1 " is shown as K.sub.1 "+D") which cancels the braking torque of the AVR 6, the total sum of torques becomes K.sub.1 +K.sub.1 '+K.sub.1 "+D+D'+D". Thus a conditon approximately identical with that in the absence of the AVR 6 is recovered for the stabilization control.
Nevertheless, it is impossible for the conventional PSS to realize the increased synchronizing power, which is needed to recover to static stabilization in a transient domain where the generator drifts excessively immediately after an accident has taken place in the power system. This is because the conventional PSS have not originally been so constructed so as to increase the synchronizing power and generally their synchronizing torque factor K.sub.1 " is very small or negative as shown in FIG. 3.
It can be concluded that a conventional power system stabilizing apparatus for a synchronous generator has problems in low transient stability.